Knowledge transfer. The mapping function \(f(\cdot )\)  serves as an implicit neural representation for the 3D environment, which can be queried at any time to predict the scene property \(\mathbf {y}\)  given the spatial coordinate \(\mathbf {x}\) . For previously visited areas \(\mathbf {x}\in \Omega ^{1:t}\) , the mapping function serves as a compact memory of past observations \(\mathcal {D}^{1:t}\) . This is related to backward transfer [1]}, [2]}, where the neural network not only memorizes existing data, but also leads to better performance on previously visited areas when learning from new observations. On the other hand, for unseen areas \(\mathbf {x} \in \mathcal {W} \cap \overline{\Omega ^{1:t}}\) , the mapping function serves as a predictor. Forward transfer may be facilitated that distills knowledge and skills for future exploration. Consequently, continual neural mapping alleviates the need for storing the entire dataset \(\mathcal {D}^{1:t}\)  while preserving the complete mapping function within the environment, guaranteeing a quick convergence to new observations.
